Finding Linear and Angular Speed? Please Help!?

Question

An object is traveling around a circle with a radius of 5 centimeters. If in 20 seconds a central angle of 1/3 radian is swept out, what is the angular speed of the object? what is the linear speed?

Thanks..

Answer 1

As a simple proportion:

1/3 radian in 20 s = 1/3 min
1 radian in 1 min., angular speed

circumference is 2πr = 10π cm
1 rotation is 2π radians, so 1 radian = 1/(2π) rotations, 1/(2π) of the circumference, or 10π/(2π) cm = 5 cm.

So linear speed is 5 cm/min.

Think about how radian measure is defined: radius laid out along the circumference of the circle.